LMFDB - Embedded newform 966.2.h.b.827.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(827,966)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			827.9
Character	$\chi$	$=$	966.827
Dual form			966.2.h.b.827.21

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.23024 - 1.21923i) q^{3} -1.00000 q^{4} -0.666555 q^{5} +(-1.21923 - 1.23024i) q^{6} -1.00000i q^{7} +1.00000i q^{8} +(0.0269708 - 2.99988i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.23024 - 1.21923i) q^{3} -1.00000 q^{4} -0.666555 q^{5} +(-1.21923 - 1.23024i) q^{6} -1.00000i q^{7} +1.00000i q^{8} +(0.0269708 - 2.99988i) q^{9} +0.666555i q^{10} -5.34963 q^{11} +(-1.23024 + 1.21923i) q^{12} +5.36659 q^{13} -1.00000 q^{14} +(-0.820021 + 0.812682i) q^{15} +1.00000 q^{16} -0.110106 q^{17} +(-2.99988 - 0.0269708i) q^{18} -7.89629i q^{19} +0.666555 q^{20} +(-1.21923 - 1.23024i) q^{21} +5.34963i q^{22} +(-3.11403 - 3.64730i) q^{23} +(1.21923 + 1.23024i) q^{24} -4.55570 q^{25} -5.36659i q^{26} +(-3.62435 - 3.72345i) q^{27} +1.00000i q^{28} +5.21125i q^{29} +(0.812682 + 0.820021i) q^{30} -6.24961 q^{31} -1.00000i q^{32} +(-6.58131 + 6.52241i) q^{33} +0.110106i q^{34} +0.666555i q^{35} +(-0.0269708 + 2.99988i) q^{36} +4.98276i q^{37} -7.89629 q^{38} +(6.60218 - 6.54309i) q^{39} -0.666555i q^{40} -10.3863i q^{41} +(-1.23024 + 1.21923i) q^{42} +7.96918i q^{43} +5.34963 q^{44} +(-0.0179775 + 1.99958i) q^{45} +(-3.64730 + 3.11403i) q^{46} +4.18892i q^{47} +(1.23024 - 1.21923i) q^{48} -1.00000 q^{49} +4.55570i q^{50} +(-0.135457 + 0.134244i) q^{51} -5.36659 q^{52} +9.76235 q^{53} +(-3.72345 + 3.62435i) q^{54} +3.56582 q^{55} +1.00000 q^{56} +(-9.62737 - 9.71432i) q^{57} +5.21125 q^{58} -2.11462i q^{59} +(0.820021 - 0.812682i) q^{60} -3.58796i q^{61} +6.24961i q^{62} +(-2.99988 - 0.0269708i) q^{63} -1.00000 q^{64} -3.57713 q^{65} +(6.52241 + 6.58131i) q^{66} -8.90006i q^{67} +0.110106 q^{68} +(-8.27789 - 0.690333i) q^{69} +0.666555 q^{70} -6.81278i q^{71} +(2.99988 + 0.0269708i) q^{72} +9.22001 q^{73} +4.98276 q^{74} +(-5.60460 + 5.55444i) q^{75} +7.89629i q^{76} +5.34963i q^{77} +(-6.54309 - 6.60218i) q^{78} -5.18489i q^{79} -0.666555 q^{80} +(-8.99855 - 0.161818i) q^{81} -10.3863 q^{82} +9.21786 q^{83} +(1.21923 + 1.23024i) q^{84} +0.0733918 q^{85} +7.96918 q^{86} +(6.35370 + 6.41108i) q^{87} -5.34963i q^{88} +3.34789 q^{89} +(1.99958 + 0.0179775i) q^{90} -5.36659i q^{91} +(3.11403 + 3.64730i) q^{92} +(-7.68851 + 7.61969i) q^{93} +4.18892 q^{94} +5.26331i q^{95} +(-1.21923 - 1.23024i) q^{96} +1.57177i q^{97} +1.00000i q^{98} +(-0.144283 + 16.0482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9	$ 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 24 q^{14} + 4 q^{15} + 24 q^{16} - 32 q^{17} + 4 q^{18} - 4 q^{20} + 8 q^{23} - 12 q^{25} + 16 q^{27} + 4 q^{30} - 16 q^{31} - 20 q^{33} + 4 q^{36} - 8 q^{39} - 4 q^{42} - 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} - 24 q^{51} - 8 q^{52} - 24 q^{53} - 12 q^{54} + 16 q^{55} + 24 q^{56} - 4 q^{57} + 4 q^{58} - 4 q^{60} + 4 q^{63} - 24 q^{64} + 12 q^{66} + 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} + 16 q^{74} + 48 q^{75} + 12 q^{78} + 4 q^{80} - 8 q^{81} - 8 q^{82} - 16 q^{83} - 16 q^{85} - 16 q^{86} + 20 q^{87} - 24 q^{89} + 28 q^{90} - 8 q^{92} + 16 q^{93} + 8 q^{94} + 48 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 24 * q^14 + 4 * q^15 + 24 * q^16 - 32 * q^17 + 4 * q^18 - 4 * q^20 + 8 * q^23 - 12 * q^25 + 16 * q^27 + 4 * q^30 - 16 * q^31 - 20 * q^33 + 4 * q^36 - 8 * q^39 - 4 * q^42 - 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 - 24 * q^51 - 8 * q^52 - 24 * q^53 - 12 * q^54 + 16 * q^55 + 24 * q^56 - 4 * q^57 + 4 * q^58 - 4 * q^60 + 4 * q^63 - 24 * q^64 + 12 * q^66 + 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 + 16 * q^74 + 48 * q^75 + 12 * q^78 + 4 * q^80 - 8 * q^81 - 8 * q^82 - 16 * q^83 - 16 * q^85 - 16 * q^86 + 20 * q^87 - 24 * q^89 + 28 * q^90 - 8 * q^92 + 16 * q^93 + 8 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.23024	−	1.21923i	0.710278	−	0.703921i
$3$	1.23024	−	1.21923i	0.710278	−	0.703921i
$4$	−1.00000			−0.500000
$5$	−0.666555			−0.298092			−0.149046	−	0.988830i	$-0.547620\pi$
$5$	−0.666555			−0.298092			−0.149046	+	0.988830i	$0.547620\pi$
$6$	−1.21923	−	1.23024i	−0.497747	−	0.502243i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			1.00000i			0.353553i
$9$	0.0269708	−	2.99988i	0.00899025	−	0.999960i
$10$			0.666555i			0.210783i
$11$	−5.34963			−1.61297			−0.806486	−	0.591253i	$-0.798634\pi$
$11$	−5.34963			−1.61297			−0.806486	+	0.591253i	$0.798634\pi$
$12$	−1.23024	+	1.21923i	−0.355139	+	0.351961i
$13$	5.36659			1.48842			0.744212	−	0.667944i	$-0.232825\pi$
$13$	5.36659			1.48842			0.744212	+	0.667944i	$0.232825\pi$
$14$	−1.00000			−0.267261
$15$	−0.820021	+	0.812682i	−0.211729	+	0.209834i
$16$	1.00000			0.250000
$17$	−0.110106			−0.0267046			−0.0133523	−	0.999911i	$-0.504250\pi$
$17$	−0.110106			−0.0267046			−0.0133523	+	0.999911i	$0.504250\pi$
$18$	−2.99988	−	0.0269708i	−0.707078	−	0.00635707i
$19$		−	7.89629i		−	1.81153i	−0.423777	−	0.905767i	$-0.639296\pi$
$19$		−	7.89629i		−	1.81153i	0.423777	−	0.905767i	$-0.360704\pi$
$20$	0.666555			0.149046
$21$	−1.21923	−	1.23024i	−0.266057	−	0.268460i
$22$			5.34963i			1.14054i
$23$	−3.11403	−	3.64730i	−0.649321	−	0.760515i
$23$	−3.11403	−	3.64730i	−0.649321	−	0.760515i
$24$	1.21923	+	1.23024i	0.248874	+	0.251121i
$25$	−4.55570			−0.911141
$26$		−	5.36659i		−	1.05247i
$27$	−3.62435	−	3.72345i	−0.697507	−	0.716578i
$28$			1.00000i			0.188982i
$29$			5.21125i			0.967705i	0.875150	+	0.483852i	$0.160763\pi$
$29$			5.21125i			0.967705i	−0.875150	+	0.483852i	$0.839237\pi$
$30$	0.812682	+	0.820021i	0.148375	+	0.149715i
$31$	−6.24961			−1.12246			−0.561231	−	0.827659i	$-0.689672\pi$
$31$	−6.24961			−1.12246			−0.561231	+	0.827659i	$0.689672\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−6.58131	+	6.52241i	−1.14566	+	1.13541i
$34$			0.110106i			0.0188830i
$35$			0.666555i			0.112668i
$36$	−0.0269708	+	2.99988i	−0.00449513	+	0.499980i
$37$			4.98276i			0.819161i	0.912274	+	0.409581i	$0.134325\pi$
$37$			4.98276i			0.819161i	−0.912274	+	0.409581i	$0.865675\pi$
$38$	−7.89629			−1.28095
$39$	6.60218	−	6.54309i	1.05719	−	1.04773i
$40$		−	0.666555i		−	0.105392i
$41$		−	10.3863i		−	1.62207i	−0.584996	−	0.811036i	$-0.698904\pi$
$41$		−	10.3863i		−	1.62207i	0.584996	−	0.811036i	$-0.301096\pi$
$42$	−1.23024	+	1.21923i	−0.189830	+	0.188131i
$43$			7.96918i			1.21529i	0.794209	+	0.607645i	$0.207885\pi$
$43$			7.96918i			1.21529i	−0.794209	+	0.607645i	$0.792115\pi$
$44$	5.34963			0.806486
$45$	−0.0179775	+	1.99958i	−0.00267993	+	0.298080i
$46$	−3.64730	+	3.11403i	−0.537765	+	0.459139i
$47$			4.18892i			0.611016i	0.952189	+	0.305508i	$0.0988263\pi$
$47$			4.18892i			0.611016i	−0.952189	+	0.305508i	$0.901174\pi$
$48$	1.23024	−	1.21923i	0.177570	−	0.175980i
$49$	−1.00000			−0.142857
$50$			4.55570i			0.644274i
$51$	−0.135457	+	0.134244i	−0.0189677	+	0.0187980i
$52$	−5.36659			−0.744212
$53$	9.76235			1.34096			0.670481	−	0.741927i	$-0.266088\pi$
$53$	9.76235			1.34096			0.670481	+	0.741927i	$0.266088\pi$
$54$	−3.72345	+	3.62435i	−0.506697	+	0.493212i
$55$	3.56582			0.480815
$56$	1.00000			0.133631
$57$	−9.62737	−	9.71432i	−1.27518	−	1.28669i
$58$	5.21125			0.684271
$59$		−	2.11462i		−	0.275300i	−0.990481	−	0.137650i	$-0.956045\pi$
$59$		−	2.11462i		−	0.275300i	0.990481	−	0.137650i	$-0.0439549\pi$
$60$	0.820021	−	0.812682i	0.105864	−	0.104917i
$61$		−	3.58796i		−	0.459391i	−0.973263	−	0.229696i	$-0.926227\pi$
$61$		−	3.58796i		−	0.459391i	0.973263	−	0.229696i	$-0.0737730\pi$
$62$			6.24961i			0.793701i
$63$	−2.99988	−	0.0269708i	−0.377949	−	0.00339800i
$64$	−1.00000			−0.125000
$65$	−3.57713			−0.443688
$66$	6.52241	+	6.58131i	0.802853	+	0.810103i
$67$		−	8.90006i		−	1.08732i	−0.839307	−	0.543658i	$-0.817039\pi$
$67$		−	8.90006i		−	1.08732i	0.839307	−	0.543658i	$-0.182961\pi$
$68$	0.110106			0.0133523
$69$	−8.27789	−	0.690333i	−0.996541	−	0.0831063i
$70$	0.666555			0.0796686
$71$		−	6.81278i		−	0.808528i	−0.914642	−	0.404264i	$-0.867528\pi$
$71$		−	6.81278i		−	0.808528i	0.914642	−	0.404264i	$-0.132472\pi$
$72$	2.99988	+	0.0269708i	0.353539	+	0.00317853i
$73$	9.22001			1.07912			0.539561	−	0.841947i	$-0.318590\pi$
$73$	9.22001			1.07912			0.539561	+	0.841947i	$0.318590\pi$
$74$	4.98276			0.579235
$75$	−5.60460	+	5.55444i	−0.647163	+	0.641371i
$76$			7.89629i			0.905767i
$77$			5.34963i			0.609646i
$78$	−6.54309	−	6.60218i	−0.740859	−	0.747549i
$79$		−	5.18489i		−	0.583345i	−0.956518	−	0.291673i	$-0.905788\pi$
$79$		−	5.18489i		−	0.583345i	0.956518	−	0.291673i	$-0.0942118\pi$
$80$	−0.666555			−0.0745231
$81$	−8.99855	−	0.161818i	−0.999838	−	0.0179798i
$82$	−10.3863			−1.14698
$83$	9.21786			1.01179			0.505896	−	0.862594i	$-0.331162\pi$
$83$	9.21786			1.01179			0.505896	+	0.862594i	$0.331162\pi$
$84$	1.21923	+	1.23024i	0.133029	+	0.134230i
$85$	0.0733918			0.00796046
$86$	7.96918			0.859339
$87$	6.35370	+	6.41108i	0.681188	+	0.687340i
$88$		−	5.34963i		−	0.570272i
$89$	3.34789			0.354875			0.177438	−	0.984132i	$-0.443219\pi$
$89$	3.34789			0.354875			0.177438	+	0.984132i	$0.443219\pi$
$90$	1.99958	+	0.0179775i	0.210775	+	0.00189499i
$91$		−	5.36659i		−	0.562571i
$92$	3.11403	+	3.64730i	0.324660	+	0.380257i
$93$	−7.68851	+	7.61969i	−0.797261	+	0.790125i
$94$	4.18892			0.432054
$95$			5.26331i			0.540004i
$96$	−1.21923	−	1.23024i	−0.124437	−	0.125561i
$97$			1.57177i			0.159589i	0.996811	+	0.0797946i	$0.0254265\pi$
$97$			1.57177i			0.159589i	−0.996811	+	0.0797946i	$0.974574\pi$
$98$			1.00000i			0.101015i
$99$	−0.144283	+	16.0482i	−0.0145010	+	1.61291i
$100$	4.55570			0.455570
$101$			5.49382i			0.546656i	0.961921	+	0.273328i	$0.0881244\pi$
$101$			5.49382i			0.546656i	−0.961921	+	0.273328i	$0.911876\pi$
$102$	0.134244	+	0.135457i	0.0132922	+	0.0134122i
$103$			13.1797i			1.29864i	0.760517	+	0.649318i	$0.224946\pi$
$103$			13.1797i			1.29864i	−0.760517	+	0.649318i	$0.775054\pi$
$104$			5.36659i			0.526237i
$105$	0.812682	+	0.820021i	0.0793096	+	0.0800259i
$106$		−	9.76235i		−	0.948203i
$107$	−9.40743			−0.909451			−0.454725	−	0.890632i	$-0.650263\pi$
$107$	−9.40743			−0.909451			−0.454725	+	0.890632i	$0.650263\pi$
$108$	3.62435	+	3.72345i	0.348754	+	0.358289i
$109$		−	17.6231i		−	1.68799i	−0.536350	−	0.843995i	$-0.680197\pi$
$109$		−	17.6231i		−	1.68799i	0.536350	−	0.843995i	$-0.319803\pi$
$110$		−	3.56582i		−	0.339988i
$111$	6.07512	+	6.12998i	0.576625	+	0.581832i
$112$		−	1.00000i		−	0.0944911i
$113$	0.0518600			0.00487857			0.00243929	−	0.999997i	$-0.499224\pi$
$113$	0.0518600			0.00487857			0.00243929	+	0.999997i	$0.499224\pi$
$114$	−9.71432	+	9.62737i	−0.909829	+	0.901686i
$115$	2.07567	+	2.43113i	0.193558	+	0.226704i
$116$		−	5.21125i		−	0.483852i
$117$	0.144741	−	16.0991i	0.0133813	−	1.48836i
$118$	−2.11462			−0.194666
$119$			0.110106i			0.0100934i
$120$	−0.812682	−	0.820021i	−0.0741874	−	0.0748574i
$121$	17.6185			1.60168
$122$	−3.58796			−0.324839
$123$	−12.6633	−	12.7777i	−1.14181	−	1.15212i
$124$	6.24961			0.561231
$125$	6.36940			0.569697
$126$	−0.0269708	+	2.99988i	−0.00240275	+	0.267250i
$127$	12.3042			1.09182			0.545912	−	0.837842i	$-0.316183\pi$
$127$	12.3042			1.09182			0.545912	+	0.837842i	$0.316183\pi$
$128$			1.00000i			0.0883883i
$129$	9.71624	+	9.80399i	0.855468	+	0.863193i
$130$			3.57713i			0.313735i
$131$			12.0793i			1.05537i	0.849439	+	0.527687i	$0.176941\pi$
$131$			12.0793i			1.05537i	−0.849439	+	0.527687i	$0.823059\pi$
$132$	6.58131	−	6.52241i	0.572830	−	0.567703i
$133$	−7.89629			−0.684695
$134$	−8.90006			−0.768848
$135$	2.41583	+	2.48188i	0.207922	+	0.213607i
$136$		−	0.110106i		−	0.00944152i
$137$	12.0653			1.03081			0.515403	−	0.856948i	$-0.327642\pi$
$137$	12.0653			1.03081			0.515403	+	0.856948i	$0.327642\pi$
$138$	−0.690333	+	8.27789i	−0.0587650	+	0.704661i
$139$	5.04057			0.427536			0.213768	−	0.976884i	$-0.431426\pi$
$139$	5.04057			0.427536			0.213768	+	0.976884i	$0.431426\pi$
$140$		−	0.666555i		−	0.0563342i
$141$	5.10724	+	5.15336i	0.430107	+	0.433991i
$142$	−6.81278			−0.571715
$143$	−28.7092			−2.40079
$144$	0.0269708	−	2.99988i	0.00224756	−	0.249990i
$145$		−	3.47358i		−	0.288466i
$146$		−	9.22001i		−	0.763054i
$147$	−1.23024	+	1.21923i	−0.101468	+	0.100560i
$148$		−	4.98276i		−	0.409581i
$149$	21.5213			1.76310			0.881548	−	0.472095i	$-0.156502\pi$
$149$	21.5213			1.76310			0.881548	+	0.472095i	$0.156502\pi$
$150$	5.55444	+	5.60460i	0.453518	+	0.457614i
$151$	3.96771			0.322887			0.161444	−	0.986882i	$-0.448385\pi$
$151$	3.96771			0.322887			0.161444	+	0.986882i	$0.448385\pi$
$152$	7.89629			0.640474
$153$	−0.00296964	+	0.330305i	−0.000240082	+	0.0267036i
$154$	5.34963			0.431085
$155$	4.16571			0.334598
$156$	−6.60218	+	6.54309i	−0.528597	+	0.523866i
$157$		−	17.1304i		−	1.36715i	−0.729879	−	0.683577i	$-0.760424\pi$
$157$		−	17.1304i		−	1.36715i	0.729879	−	0.683577i	$-0.239576\pi$
$158$	−5.18489			−0.412488
$159$	12.0100	−	11.9025i	0.952456	−	0.943931i
$160$			0.666555i			0.0526958i
$161$	−3.64730	+	3.11403i	−0.287448	+	0.245420i
$162$	−0.161818	+	8.99855i	−0.0127136	+	0.706992i
$163$	−23.2565			−1.82159			−0.910795	−	0.412858i	$-0.864530\pi$
$163$	−23.2565			−1.82159			−0.910795	+	0.412858i	$0.864530\pi$
$164$			10.3863i			0.811036i
$165$	4.38681	−	4.34754i	0.341512	−	0.338456i
$166$		−	9.21786i		−	0.715445i
$167$		−	1.07849i		−	0.0834558i	−0.999129	−	0.0417279i	$-0.986714\pi$
$167$		−	1.07849i		−	0.0834558i	0.999129	−	0.0417279i	$-0.0132863\pi$
$168$	1.23024	−	1.21923i	0.0949149	−	0.0940654i
$169$	15.8003			1.21540
$170$		−	0.0733918i		−	0.00562889i
$171$	−23.6879	−	0.212969i	−1.81146	−	0.0162861i
$172$		−	7.96918i		−	0.607645i
$173$		−	3.31012i		−	0.251664i	−0.992052	−	0.125832i	$-0.959840\pi$
$173$		−	3.31012i		−	0.251664i	0.992052	−	0.125832i	$-0.0401600\pi$
$174$	6.41108	−	6.35370i	0.486022	−	0.481672i
$175$			4.55570i			0.344379i
$176$	−5.34963			−0.403243
$177$	−2.57820	−	2.60148i	−0.193789	−	0.195539i
$178$		−	3.34789i		−	0.250935i
$179$		−	16.5448i		−	1.23661i	−0.785937	−	0.618307i	$-0.787819\pi$
$179$		−	16.5448i		−	1.23661i	0.785937	−	0.618307i	$-0.212181\pi$
$180$	0.0179775	−	1.99958i	0.00133996	−	0.149040i
$181$		−	7.95913i		−	0.591597i	−0.955250	−	0.295799i	$-0.904414\pi$
$181$		−	7.95913i		−	0.591597i	0.955250	−	0.295799i	$-0.0955858\pi$
$182$	−5.36659			−0.397798
$183$	−4.37454	−	4.41404i	−0.323375	−	0.326295i
$184$	3.64730	−	3.11403i	0.268883	−	0.229570i
$185$		−	3.32129i		−	0.244186i
$186$	7.61969	+	7.68851i	0.558703	+	0.563749i
$187$	0.589026			0.0430739
$188$		−	4.18892i		−	0.305508i
$189$	−3.72345	+	3.62435i	−0.270841	+	0.263633i
$190$	5.26331			0.381841
$191$	−12.4324			−0.899574			−0.449787	−	0.893136i	$-0.648500\pi$
$191$	−12.4324			−0.899574			−0.449787	+	0.893136i	$0.648500\pi$
$192$	−1.23024	+	1.21923i	−0.0887848	+	0.0879901i
$193$	−18.3412			−1.32023			−0.660115	−	0.751165i	$-0.729492\pi$
$193$	−18.3412			−1.32023			−0.660115	+	0.751165i	$0.729492\pi$
$194$	1.57177			0.112847
$195$	−4.40072	+	4.36133i	−0.315142	+	0.312321i
$196$	1.00000			0.0714286
$197$			3.51591i			0.250498i	0.992125	+	0.125249i	$0.0399730\pi$
$197$			3.51591i			0.250498i	−0.992125	+	0.125249i	$0.960027\pi$
$198$	16.0482	+	0.144283i	1.14050	+	0.0102538i
$199$		−	5.43544i		−	0.385308i	−0.981267	−	0.192654i	$-0.938290\pi$
$199$		−	5.43544i		−	0.385308i	0.981267	−	0.192654i	$-0.0617096\pi$
$200$		−	4.55570i		−	0.322137i
$201$	−10.8512	−	10.9492i	−0.765385	−	0.772297i
$202$	5.49382			0.386544
$203$	5.21125			0.365758
$204$	0.135457	−	0.134244i	0.00948387	−	0.00939898i
$205$			6.92306i			0.483528i
$206$	13.1797			0.918275
$207$	−11.0254	+	9.24335i	−0.766321	+	0.642457i
$208$	5.36659			0.372106
$209$			42.2422i			2.92195i
$210$	0.820021	−	0.812682i	0.0565868	−	0.0560804i
$211$	11.3045			0.778237			0.389119	−	0.921188i	$-0.372780\pi$
$211$	11.3045			0.778237			0.389119	+	0.921188i	$0.372780\pi$
$212$	−9.76235			−0.670481
$213$	−8.30632	−	8.38133i	−0.569140	−	0.574280i
$214$			9.40743i			0.643079i
$215$		−	5.31190i		−	0.362269i
$216$	3.72345	−	3.62435i	0.253349	−	0.246606i
$217$			6.24961i			0.424251i
$218$	−17.6231			−1.19359
$219$	11.3428	−	11.2413i	0.766476	−	0.759616i
$220$	−3.56582			−0.240408
$221$	−0.590894			−0.0397478
$222$	6.12998	−	6.07512i	0.411418	−	0.407735i
$223$	19.8306			1.32795			0.663976	−	0.747754i	$-0.268868\pi$
$223$	19.8306			1.32795			0.663976	+	0.747754i	$0.268868\pi$
$224$	−1.00000			−0.0668153
$225$	−0.122871	+	13.6666i	−0.00819139	+	0.911104i
$226$		−	0.0518600i		−	0.00344967i
$227$	27.0595			1.79600			0.898002	−	0.439991i	$-0.145018\pi$
$227$	27.0595			1.79600			0.898002	+	0.439991i	$0.145018\pi$
$228$	9.62737	+	9.71432i	0.637588	+	0.643346i
$229$		−	3.94506i		−	0.260697i	−0.991468	−	0.130349i	$-0.958390\pi$
$229$		−	3.94506i		−	0.260697i	0.991468	−	0.130349i	$-0.0416096\pi$
$230$	2.43113	−	2.07567i	0.160304	−	0.136866i
$231$	6.52241	+	6.58131i	0.429143	+	0.433019i
$232$	−5.21125			−0.342135
$233$		−	11.1651i		−	0.731450i	−0.930723	−	0.365725i	$-0.880821\pi$
$233$		−	11.1651i		−	0.731450i	0.930723	−	0.365725i	$-0.119179\pi$
$234$	−16.0991	−	0.144741i	−1.05243	−	0.00946201i
$235$		−	2.79214i		−	0.182139i
$236$			2.11462i			0.137650i
$237$	−6.32156	−	6.37865i	−0.410629	−	0.414338i
$238$	0.110106			0.00713712
$239$		−	11.2107i		−	0.725162i	−0.931952	−	0.362581i	$-0.881896\pi$
$239$		−	11.2107i		−	0.725162i	0.931952	−	0.362581i	$-0.118104\pi$
$240$	−0.820021	+	0.812682i	−0.0529322	+	0.0524584i
$241$		−	0.654051i		−	0.0421311i	−0.999778	−	0.0210656i	$-0.993294\pi$
$241$		−	0.654051i		−	0.0421311i	0.999778	−	0.0210656i	$-0.00670587\pi$
$242$		−	17.6185i		−	1.13256i
$243$	−11.2676	+	10.7722i	−0.722820	+	0.691037i
$244$			3.58796i			0.229696i
$245$	0.666555			0.0425846
$246$	−12.7777	+	12.6633i	−0.814674	+	0.807382i
$247$		−	42.3761i		−	2.69633i
$248$		−	6.24961i		−	0.396851i
$249$	11.3402	−	11.2387i	0.718654	−	0.712222i
$250$		−	6.36940i		−	0.402836i
$251$	−14.7422			−0.930522			−0.465261	−	0.885173i	$-0.654040\pi$
$251$	−14.7422			−0.930522			−0.465261	+	0.885173i	$0.654040\pi$
$252$	2.99988	+	0.0269708i	0.188975	+	0.00169900i
$253$	16.6589	+	19.5117i	1.04734	+	1.22669i
$254$		−	12.3042i		−	0.772037i
$255$	0.0902893	−	0.0894812i	0.00565414	−	0.00560353i
$256$	1.00000			0.0625000
$257$			0.00767116i			0.000478514i	1.00000		0.000239257i	$7.61578e-5\pi$
$257$			0.00767116i			0.000478514i	−1.00000		0.000239257i	$0.999924\pi$
$258$	9.80399	−	9.71624i	0.610370	−	0.604907i
$259$	4.98276			0.309614
$260$	3.57713			0.221844
$261$	15.6331	+	0.140551i	0.967666	+	0.00869991i
$262$	12.0793			0.746262
$263$	18.2891			1.12775			0.563877	−	0.825859i	$-0.309309\pi$
$263$	18.2891			1.12775			0.563877	+	0.825859i	$0.309309\pi$
$264$	−6.52241	−	6.58131i	−0.401426	−	0.405052i
$265$	−6.50714			−0.399731
$266$			7.89629i			0.484153i
$267$	4.11870	−	4.08184i	0.252060	−	0.249804i
$268$			8.90006i			0.543658i
$269$			3.61332i			0.220308i	0.993915	+	0.110154i	$0.0351344\pi$
$269$			3.61332i			0.220308i	−0.993915	+	0.110154i	$0.964866\pi$
$270$	2.48188	−	2.41583i	0.151043	−	0.147023i
$271$	12.1641			0.738916			0.369458	−	0.929247i	$-0.379543\pi$
$271$	12.1641			0.738916			0.369458	+	0.929247i	$0.379543\pi$
$272$	−0.110106			−0.00667616
$273$	−6.54309	−	6.60218i	−0.396006	−	0.399582i
$274$		−	12.0653i		−	0.728889i
$275$	24.3713			1.46965
$276$	8.27789	+	0.690333i	0.498270	+	0.0415532i
$277$	16.8767			1.01402			0.507012	−	0.861939i	$-0.330750\pi$
$277$	16.8767			1.01402			0.507012	+	0.861939i	$0.330750\pi$
$278$		−	5.04057i		−	0.302313i
$279$	−0.168557	+	18.7481i	−0.0100912	+	1.12242i
$280$	−0.666555			−0.0398343
$281$	27.1477			1.61950			0.809749	−	0.586776i	$-0.199603\pi$
$281$	27.1477			1.61950			0.809749	+	0.586776i	$0.199603\pi$
$282$	5.15336	−	5.10724i	0.306878	−	0.304132i
$283$		−	8.86381i		−	0.526899i	−0.964673	−	0.263449i	$-0.915140\pi$
$283$		−	8.86381i		−	0.526899i	0.964673	−	0.263449i	$-0.0848602\pi$
$284$			6.81278i			0.404264i
$285$	6.41717	+	6.47513i	0.380120	+	0.383553i
$286$			28.7092i			1.69761i
$287$	−10.3863			−0.613086
$288$	−2.99988	−	0.0269708i	−0.176770	−	0.00158927i
$289$	−16.9879			−0.999287
$290$	−3.47358			−0.203976
$291$	1.91635	+	1.93365i	0.112338	+	0.113353i
$292$	−9.22001			−0.539561
$293$	−27.7456			−1.62092			−0.810458	−	0.585797i	$-0.800782\pi$
$293$	−27.7456			−1.62092			−0.810458	+	0.585797i	$0.800782\pi$
$294$	1.21923	+	1.23024i	0.0711068	+	0.0717489i
$295$			1.40951i			0.0820648i
$296$	−4.98276			−0.289617
$297$	19.3889	+	19.9191i	1.12506	+	1.15582i
$298$		−	21.5213i		−	1.24670i
$299$	−16.7117	−	19.5736i	−0.966464	−	1.13197i
$300$	5.60460	−	5.55444i	0.323582	−	0.320686i
$301$	7.96918			0.459336
$302$		−	3.96771i		−	0.228316i
$303$	6.69822	+	6.75871i	0.384802	+	0.388278i
$304$		−	7.89629i		−	0.452883i
$305$			2.39157i			0.136941i
$306$	0.330305	+	0.00296964i	0.0188823	+	0.000169763i
$307$	33.1791			1.89363			0.946815	−	0.321779i	$-0.104281\pi$
$307$	33.1791			1.89363			0.946815	+	0.321779i	$0.104281\pi$
$308$		−	5.34963i		−	0.304823i
$309$	16.0691	+	16.2142i	0.914137	+	0.922393i
$310$		−	4.16571i		−	0.236596i
$311$			15.0871i			0.855509i	0.903895	+	0.427755i	$0.140695\pi$
$311$			15.0871i			0.855509i	−0.903895	+	0.427755i	$0.859305\pi$
$312$	6.54309	+	6.60218i	0.370429	+	0.373775i
$313$			25.3150i			1.43089i	0.698669	+	0.715445i	$0.253776\pi$
$313$			25.3150i			1.43089i	−0.698669	+	0.715445i	$0.746224\pi$
$314$	−17.1304			−0.966723
$315$	1.99958	+	0.0179775i	0.112664	+	0.00101292i
$316$			5.18489i			0.291673i
$317$			20.1209i			1.13010i	0.825056	+	0.565050i	$0.191143\pi$
$317$			20.1209i			1.13010i	−0.825056	+	0.565050i	$0.808857\pi$
$318$	−11.9025	−	12.0100i	−0.667460	−	0.673488i
$319$		−	27.8782i		−	1.56088i
$320$	0.666555			0.0372616
$321$	−11.5734	+	11.4698i	−0.645963	+	0.640182i
$322$	3.11403	+	3.64730i	0.173538	+	0.203256i
$323$			0.869430i			0.0483764i
$324$	8.99855	+	0.161818i	0.499919	+	0.00898989i
$325$	−24.4486			−1.35616
$326$			23.2565i			1.28806i
$327$	−21.4866	−	21.6807i	−1.18821	−	1.19894i
$328$	10.3863			0.573489
$329$	4.18892			0.230942
$330$	−4.34754	−	4.38681i	−0.239324	−	0.241486i
$331$	−13.2669			−0.729212			−0.364606	−	0.931162i	$-0.618796\pi$
$331$	−13.2669			−0.729212			−0.364606	+	0.931162i	$0.618796\pi$
$332$	−9.21786			−0.505896
$333$	14.9477	+	0.134389i	0.819128	+	0.00736447i
$334$	−1.07849			−0.0590122
$335$			5.93238i			0.324121i
$336$	−1.21923	−	1.23024i	−0.0665143	−	0.0671150i
$337$			9.04921i			0.492942i	0.969150	+	0.246471i	$0.0792710\pi$
$337$			9.04921i			0.492942i	−0.969150	+	0.246471i	$0.920729\pi$
$338$		−	15.8003i		−	0.859420i
$339$	0.0638001	−	0.0632291i	0.00346515	−	0.00343413i
$340$	−0.0733918			−0.00398023
$341$	33.4331			1.81050
$342$	−0.212969	+	23.6879i	−0.0115160	+	1.28090i
$343$			1.00000i			0.0539949i
$344$	−7.96918			−0.429670
$345$	5.51767	+	0.460145i	0.297061	+	0.0247734i
$346$	−3.31012			−0.177953
$347$		−	1.98637i		−	0.106634i	−0.998578	−	0.0533171i	$-0.983021\pi$
$347$		−	1.98637i		−	0.106634i	0.998578	−	0.0533171i	$-0.0169794\pi$
$348$	−6.35370	−	6.41108i	−0.340594	−	0.343670i
$349$	−19.8108			−1.06045			−0.530225	−	0.847857i	$-0.677893\pi$
$349$	−19.8108			−1.06045			−0.530225	+	0.847857i	$0.677893\pi$
$350$	4.55570			0.243513
$351$	−19.4504	−	19.9822i	−1.03819	−	1.06657i
$352$			5.34963i			0.285136i
$353$			26.9844i			1.43623i	0.695922	+	0.718117i	$0.254996\pi$
$353$			26.9844i			1.43623i	−0.695922	+	0.718117i	$0.745004\pi$
$354$	−2.60148	+	2.57820i	−0.138267	+	0.137030i
$355$			4.54109i			0.241016i
$356$	−3.34789			−0.177438
$357$	0.134244	+	0.135457i	0.00710496	+	0.00716913i
$358$	−16.5448			−0.874418
$359$	14.2075			0.749845			0.374923	−	0.927056i	$-0.377669\pi$
$359$	14.2075			0.749845			0.374923	+	0.927056i	$0.377669\pi$
$360$	−1.99958	−	0.0179775i	−0.105387	−	0.000947497i
$361$	−43.3514			−2.28165
$362$	−7.95913			−0.418323
$363$	21.6749	−	21.4809i	1.13764	−	1.12746i
$364$			5.36659i			0.281286i
$365$	−6.14565			−0.321678
$366$	−4.41404	+	4.37454i	−0.230726	+	0.228661i
$367$			12.5018i			0.652589i	0.945268	+	0.326295i	$0.105800\pi$
$367$			12.5018i			0.652589i	−0.945268	+	0.326295i	$0.894200\pi$
$368$	−3.11403	−	3.64730i	−0.162330	−	0.190129i
$369$	−31.1577	−	0.280127i	−1.62201	−	0.0145828i
$370$	−3.32129			−0.172665
$371$		−	9.76235i		−	0.506836i
$372$	7.68851	−	7.61969i	0.398630	−	0.395063i
$373$		−	30.0466i		−	1.55575i	−0.628416	−	0.777877i	$-0.716296\pi$
$373$		−	30.0466i		−	1.55575i	0.628416	−	0.777877i	$-0.283704\pi$
$374$		−	0.589026i		−	0.0304578i
$375$	7.83588	−	7.76575i	0.404643	−	0.401022i
$376$	−4.18892			−0.216027
$377$			27.9666i			1.44035i
$378$	3.62435	+	3.72345i	0.186417	+	0.191514i
$379$			6.01528i			0.308984i	0.987994	+	0.154492i	$0.0493741\pi$
$379$			6.01528i			0.308984i	−0.987994	+	0.154492i	$0.950626\pi$
$380$		−	5.26331i		−	0.270002i
$381$	15.1371	−	15.0017i	0.775499	−	0.768558i
$382$			12.4324i			0.636095i
$383$	−9.66651			−0.493935			−0.246968	−	0.969024i	$-0.579434\pi$
$383$	−9.66651			−0.493935			−0.246968	+	0.969024i	$0.579434\pi$
$384$	1.21923	+	1.23024i	0.0622184	+	0.0627803i
$385$		−	3.56582i		−	0.181731i
$386$			18.3412i			0.933543i
$387$	23.9066	+	0.214935i	1.21524	+	0.0109258i
$388$		−	1.57177i		−	0.0797946i
$389$	−15.2370			−0.772544			−0.386272	−	0.922385i	$-0.626237\pi$
$389$	−15.2370			−0.772544			−0.386272	+	0.922385i	$0.626237\pi$
$390$	4.36133	+	4.40072i	0.220844	+	0.222839i
$391$	0.342874	+	0.401590i	0.0173399	+	0.0203093i
$392$		−	1.00000i		−	0.0505076i
$393$	14.7274	+	14.8604i	0.742900	+	0.749610i
$394$	3.51591			0.177129
$395$			3.45601i			0.173891i
$396$	0.144283	−	16.0482i	0.00725052	−	0.806454i
$397$	−9.78621			−0.491156			−0.245578	−	0.969377i	$-0.578978\pi$
$397$	−9.78621			−0.491156			−0.245578	+	0.969377i	$0.578978\pi$
$398$	−5.43544			−0.272454
$399$	−9.71432	+	9.62737i	−0.486324	+	0.481971i
$400$	−4.55570			−0.227785
$401$	32.1639			1.60619			0.803095	−	0.595851i	$-0.203185\pi$
$401$	32.1639			1.60619			0.803095	+	0.595851i	$0.203185\pi$
$402$	−10.9492	+	10.8512i	−0.546096	+	0.541209i
$403$	−33.5391			−1.67070
$404$		−	5.49382i		−	0.273328i
$405$	5.99803	+	0.107861i	0.298044	+	0.00535964i
$406$		−	5.21125i		−	0.258630i
$407$		−	26.6559i		−	1.32128i
$408$	−0.134244	−	0.135457i	−0.00664608	−	0.00670611i
$409$	−1.12230			−0.0554943			−0.0277472	−	0.999615i	$-0.508833\pi$
$409$	−1.12230			−0.0554943			−0.0277472	+	0.999615i	$0.508833\pi$
$410$	6.92306			0.341906
$411$	14.8431	−	14.7103i	0.732159	−	0.725606i
$412$		−	13.1797i		−	0.649318i
$413$	−2.11462			−0.104054
$414$	9.24335	+	11.0254i	0.454286	+	0.541871i
$415$	−6.14421			−0.301608
$416$		−	5.36659i		−	0.263119i
$417$	6.20110	−	6.14560i	0.303669	−	0.300951i
$418$	42.2422			2.06613
$419$	−15.3482			−0.749807			−0.374903	−	0.927064i	$-0.622324\pi$
$419$	−15.3482			−0.749807			−0.374903	+	0.927064i	$0.622324\pi$
$420$	−0.812682	−	0.820021i	−0.0396548	−	0.0400129i
$421$			23.1332i			1.12744i	0.825965	+	0.563721i	$0.190631\pi$
$421$			23.1332i			1.12744i	−0.825965	+	0.563721i	$0.809369\pi$
$422$		−	11.3045i		−	0.550297i
$423$	12.5662	+	0.112978i	0.610991	+	0.00549319i
$424$			9.76235i			0.474101i
$425$	0.501611			0.0243317
$426$	−8.38133	+	8.30632i	−0.406077	+	0.402443i
$427$	−3.58796			−0.173633
$428$	9.40743			0.454725
$429$	−35.3192	+	35.0031i	−1.70523	+	1.68996i
$430$	−5.31190			−0.256163
$431$	−20.8892			−1.00620			−0.503098	−	0.864229i	$-0.667807\pi$
$431$	−20.8892			−1.00620			−0.503098	+	0.864229i	$0.667807\pi$
$432$	−3.62435	−	3.72345i	−0.174377	−	0.179144i
$433$			23.7880i			1.14318i	0.820540	+	0.571590i	$0.193673\pi$
$433$			23.7880i			1.14318i	−0.820540	+	0.571590i	$0.806327\pi$
$434$	6.24961			0.299991
$435$	−4.23509	−	4.27334i	−0.203057	−	0.204891i
$436$			17.6231i			0.843995i
$437$	−28.8001	+	24.5893i	−1.37770	+	1.17627i
$438$	−11.2413	−	11.3428i	−0.537130	−	0.541980i
$439$	1.21747			0.0581065			0.0290532	−	0.999578i	$-0.490751\pi$
$439$	1.21747			0.0581065			0.0290532	+	0.999578i	$0.490751\pi$
$440$			3.56582i			0.169994i
$441$	−0.0269708	+	2.99988i	−0.00128432	+	0.142851i
$442$			0.590894i			0.0281060i
$443$		−	16.8190i		−	0.799096i	−0.916712	−	0.399548i	$-0.869167\pi$
$443$		−	16.8190i		−	0.799096i	0.916712	−	0.399548i	$-0.130833\pi$
$444$	−6.07512	−	6.12998i	−0.288312	−	0.290916i
$445$	−2.23155			−0.105786
$446$		−	19.8306i		−	0.939004i
$447$	26.4763	−	26.2394i	1.25229	−	1.24108i
$448$			1.00000i			0.0472456i
$449$		−	15.8862i		−	0.749716i	−0.927082	−	0.374858i	$-0.877692\pi$
$449$		−	15.8862i		−	0.749716i	0.927082	−	0.374858i	$-0.122308\pi$
$450$	13.6666	+	0.122871i	0.644248	+	0.00579218i
$451$			55.5630i			2.61636i
$452$	−0.0518600			−0.00243929
$453$	4.88122	−	4.83754i	0.229340	−	0.227287i
$454$		−	27.0595i		−	1.26997i
$455$			3.57713i			0.167698i
$456$	9.71432	−	9.62737i	0.454914	−	0.450843i
$457$			40.2479i			1.88272i	0.337410	+	0.941358i	$0.390449\pi$
$457$			40.2479i			1.88272i	−0.337410	+	0.941358i	$0.609551\pi$
$458$	−3.94506			−0.184341
$459$	0.399063	+	0.409974i	0.0186267	+	0.0191360i
$460$	−2.07567	−	2.43113i	−0.0967788	−	0.113352i
$461$		−	12.1963i		−	0.568039i	−0.958819	−	0.284020i	$-0.908332\pi$
$461$		−	12.1963i		−	0.568039i	0.958819	−	0.284020i	$-0.0916680\pi$
$462$	6.58131	−	6.52241i	0.306190	−	0.303450i
$463$	19.8584			0.922898			0.461449	−	0.887167i	$-0.347330\pi$
$463$	19.8584			0.922898			0.461449	+	0.887167i	$0.347330\pi$
$464$			5.21125i			0.241926i
$465$	5.12481	−	5.07894i	0.237657	−	0.235530i
$466$	−11.1651			−0.517213
$467$	−9.92975			−0.459494			−0.229747	−	0.973250i	$-0.573790\pi$
$467$	−9.92975			−0.459494			−0.229747	+	0.973250i	$0.573790\pi$
$468$	−0.144741	+	16.0991i	−0.00669065	+	0.744182i
$469$	−8.90006			−0.410967
$470$	−2.79214			−0.128792
$471$	−20.8858	−	21.0744i	−0.962368	−	0.971059i
$472$	2.11462			0.0973331
$473$		−	42.6321i		−	1.96023i
$474$	−6.37865	+	6.32156i	−0.292981	+	0.290359i
$475$			35.9732i			1.65056i
$476$		−	0.110106i		−	0.00504670i
$477$	0.263298	−	29.2859i	0.0120556	−	1.34091i
$478$	−11.2107			−0.512767
$479$	13.8661			0.633558			0.316779	−	0.948499i	$-0.397399\pi$
$479$	13.8661			0.633558			0.316779	+	0.948499i	$0.397399\pi$
$480$	0.812682	+	0.820021i	0.0370937	+	0.0374287i
$481$			26.7404i			1.21926i
$482$	−0.654051			−0.0297912
$483$	−0.690333	+	8.27789i	−0.0314112	+	0.376657i
$484$	−17.6185			−0.800840
$485$		−	1.04767i		−	0.0475724i
$486$	10.7722	+	11.2676i	0.488637	+	0.511111i
$487$	−11.2926			−0.511714			−0.255857	−	0.966715i	$-0.582358\pi$
$487$	−11.2926			−0.511714			−0.255857	+	0.966715i	$0.582358\pi$
$488$	3.58796			0.162419
$489$	−28.6110	+	28.3550i	−1.29384	+	1.28226i
$490$		−	0.666555i		−	0.0301119i
$491$			12.9002i			0.582177i	0.956696	+	0.291088i	$0.0940174\pi$
$491$			12.9002i			0.582177i	−0.956696	+	0.291088i	$0.905983\pi$
$492$	12.6633	+	12.7777i	0.570905	+	0.576061i
$493$		−	0.573790i		−	0.0258422i
$494$	−42.3761			−1.90659
$495$	0.0961729	−	10.6970i	0.00432265	−	0.480796i
$496$	−6.24961			−0.280616
$497$	−6.81278			−0.305595
$498$	−11.2387	−	11.3402i	−0.503617	−	0.508165i
$499$	−0.583048			−0.0261008			−0.0130504	−	0.999915i	$-0.504154\pi$
$499$	−0.583048			−0.0261008			−0.0130504	+	0.999915i	$0.504154\pi$
$500$	−6.36940			−0.284848
$501$	−1.31492	−	1.32680i	−0.0587463	−	0.0592769i
$502$			14.7422i			0.657979i
$503$	−42.2625			−1.88439			−0.942197	−	0.335060i	$-0.891243\pi$
$503$	−42.2625			−1.88439			−0.942197	+	0.335060i	$0.891243\pi$
$504$	0.0269708	−	2.99988i	0.00120137	−	0.133625i
$505$		−	3.66194i		−	0.162954i
$506$	19.5117	−	16.6589i	0.867400	−	0.740579i
$507$	19.4381	−	19.2641i	0.863275	−	0.855548i
$508$	−12.3042			−0.545912
$509$			14.5550i			0.645140i	0.946546	+	0.322570i	$0.104547\pi$
$509$			14.5550i			0.645140i	−0.946546	+	0.322570i	$0.895453\pi$
$510$	−0.0894812	−	0.0902893i	−0.00396230	−	0.00399808i
$511$		−	9.22001i		−	0.407869i
$512$		−	1.00000i		−	0.0441942i
$513$	−29.4014	+	28.6189i	−1.29810	+	1.26356i
$514$	0.00767116			0.000338360
$515$		−	8.78501i		−	0.387114i
$516$	−9.71624	−	9.80399i	−0.427734	−	0.431597i
$517$		−	22.4091i		−	0.985552i
$518$		−	4.98276i		−	0.218930i
$519$	−4.03579	−	4.07224i	−0.177152	−	0.178752i
$520$		−	3.57713i		−	0.156867i
$521$	−4.97513			−0.217965			−0.108982	−	0.994044i	$-0.534759\pi$
$521$	−4.97513			−0.217965			−0.108982	+	0.994044i	$0.534759\pi$
$522$	0.140551	−	15.6331i	0.00615176	−	0.684243i
$523$		−	33.8532i		−	1.48030i	−0.672444	−	0.740148i	$-0.734755\pi$
$523$		−	33.8532i		−	1.48030i	0.672444	−	0.740148i	$-0.265245\pi$
$524$		−	12.0793i		−	0.527687i
$525$	5.55444	+	5.60460i	0.242416	+	0.244605i
$526$		−	18.2891i		−	0.797443i
$527$	0.688120			0.0299750
$528$	−6.58131	+	6.52241i	−0.286415	+	0.283851i
$529$	−3.60559	+	22.7156i	−0.156765	+	0.987636i
$530$			6.50714i			0.282652i
$531$	−6.34360	−	0.0570328i	−0.275289	−	0.00247501i
$532$	7.89629			0.342348
$533$		−	55.7391i		−	2.41433i
$534$	−4.08184	−	4.11870i	−0.176638	−	0.178234i
$535$	6.27057			0.271100
$536$	8.90006			0.384424
$537$	−20.1718	−	20.3540i	−0.870479	−	0.878340i
$538$	3.61332			0.155781
$539$	5.34963			0.230425
$540$	−2.41583	−	2.48188i	−0.103961	−	0.106803i
$541$	−22.8108			−0.980714			−0.490357	−	0.871522i	$-0.663134\pi$
$541$	−22.8108			−0.980714			−0.490357	+	0.871522i	$0.663134\pi$
$542$		−	12.1641i		−	0.522493i
$543$	−9.70398	−	9.79162i	−0.416438	−	0.420199i
$544$			0.110106i			0.00472076i
$545$			11.7468i			0.503177i
$546$	−6.60218	+	6.54309i	−0.282547	+	0.280018i
$547$	−17.9881			−0.769117			−0.384558	−	0.923101i	$-0.625646\pi$
$547$	−17.9881			−0.769117			−0.384558	+	0.923101i	$0.625646\pi$
$548$	−12.0653			−0.515403
$549$	−10.7634	−	0.0967700i	−0.459372	−	0.00413004i
$550$		−	24.3713i		−	1.03920i
$551$	41.1495			1.75303
$552$	0.690333	−	8.27789i	0.0293825	−	0.352330i
$553$	−5.18489			−0.220484
$554$		−	16.8767i		−	0.717023i
$555$	−4.04940	−	4.08597i	−0.171888	−	0.173440i
$556$	−5.04057			−0.213768
$557$	23.4067			0.991775			0.495887	−	0.868387i	$-0.334843\pi$
$557$	23.4067			0.991775			0.495887	+	0.868387i	$0.334843\pi$
$558$	18.7481	+	0.168557i	0.793669	+	0.00713557i
$559$			42.7673i			1.80886i
$560$			0.666555i			0.0281671i
$561$	0.724643	−	0.718157i	0.0305944	−	0.0303206i
$562$		−	27.1477i		−	1.14516i
$563$	−21.4944			−0.905880			−0.452940	−	0.891541i	$-0.649625\pi$
$563$	−21.4944			−0.905880			−0.452940	+	0.891541i	$0.649625\pi$
$564$	−5.10724	−	5.15336i	−0.215054	−	0.216996i
$565$	−0.0345675			−0.00145427
$566$	−8.86381			−0.372574
$567$	−0.161818	+	8.99855i	−0.00679572	+	0.377903i
$568$	6.81278			0.285858
$569$	−24.3265			−1.01982			−0.509910	−	0.860227i	$-0.670321\pi$
$569$	−24.3265			−1.01982			−0.509910	+	0.860227i	$0.670321\pi$
$570$	6.47513	−	6.41717i	0.271213	−	0.268786i
$571$			27.7424i			1.16098i	0.814267	+	0.580491i	$0.197139\pi$
$571$			27.7424i			1.16098i	−0.814267	+	0.580491i	$0.802861\pi$
$572$	28.7092			1.20039
$573$	−15.2948	+	15.1579i	−0.638948	+	0.633229i
$574$			10.3863i			0.433517i
$575$	14.1866	+	16.6160i	0.591623	+	0.692936i
$576$	−0.0269708	+	2.99988i	−0.00112378	+	0.124995i
$577$	29.3156			1.22042			0.610212	−	0.792238i	$-0.291084\pi$
$577$	29.3156			1.22042			0.610212	+	0.792238i	$0.291084\pi$
$578$			16.9879i			0.706603i
$579$	−22.5640	+	22.3621i	−0.937730	+	0.929337i
$580$			3.47358i			0.144233i
$581$		−	9.21786i		−	0.382421i
$582$	1.93365	−	1.91635i	0.0801525	−	0.0794351i
$583$	−52.2249			−2.16293
$584$			9.22001i			0.381527i
$585$	−0.0964778	+	10.7309i	−0.00398887	+	0.443670i
$586$			27.7456i			1.14616i
$587$			42.0361i			1.73501i	0.497425	+	0.867507i	$0.334279\pi$
$587$			42.0361i			1.73501i	−0.497425	+	0.867507i	$0.665721\pi$
$588$	1.23024	−	1.21923i	0.0507342	−	0.0502801i
$589$			49.3487i			2.03338i
$590$	1.40951			0.0580286
$591$	4.28669	+	4.32540i	0.176331	+	0.177923i
$592$			4.98276i			0.204790i
$593$			28.1606i			1.15642i	0.815890	+	0.578208i	$0.196248\pi$
$593$			28.1606i			1.15642i	−0.815890	+	0.578208i	$0.803752\pi$
$594$	19.9191	−	19.3889i	0.817289	−	0.795537i
$595$		−	0.0733918i		−	0.00300877i
$596$	−21.5213			−0.881548
$597$	−6.62704	−	6.68689i	−0.271227	−	0.273676i
$598$	−19.5736	+	16.7117i	−0.800422	+	0.683393i
$599$			3.55422i			0.145221i	0.997360	+	0.0726107i	$0.0231331\pi$
$599$			3.55422i			0.145221i	−0.997360	+	0.0726107i	$0.976867\pi$
$600$	−5.55444	−	5.60460i	−0.226759	−	0.228807i
$601$	−33.2270			−1.35536			−0.677678	−	0.735359i	$-0.737014\pi$
$601$	−33.2270			−1.35536			−0.677678	+	0.735359i	$0.737014\pi$
$602$		−	7.96918i		−	0.324800i
$603$	−26.6991	−	0.240041i	−1.08727	−	0.00977524i
$604$	−3.96771			−0.161444
$605$	−11.7437			−0.477449
$606$	6.75871	−	6.69822i	0.274554	−	0.272096i
$607$	24.3745			0.989332			0.494666	−	0.869083i	$-0.335290\pi$
$607$	24.3745			0.989332			0.494666	+	0.869083i	$0.335290\pi$
$608$	−7.89629			−0.320237
$609$	6.41108	−	6.35370i	0.259790	−	0.257465i
$610$	2.39157			0.0968319
$611$			22.4802i			0.909451i
$612$	0.00296964	−	0.330305i	0.000120041	−	0.0133518i
$613$		−	33.0981i		−	1.33682i	−0.743793	−	0.668410i	$-0.766975\pi$
$613$		−	33.0981i		−	1.33682i	0.743793	−	0.668410i	$-0.233025\pi$
$614$		−	33.1791i		−	1.33900i
$615$	8.44078	+	8.51701i	0.340365	+	0.343439i
$616$	−5.34963			−0.215543
$617$	33.8820			1.36404			0.682019	−	0.731334i	$-0.261102\pi$
$617$	33.8820			1.36404			0.682019	+	0.731334i	$0.261102\pi$
$618$	16.2142	−	16.0691i	0.652230	−	0.646393i
$619$			16.0670i			0.645789i	0.946435	+	0.322895i	$0.104656\pi$
$619$			16.0670i			0.645789i	−0.946435	+	0.322895i	$0.895344\pi$
$620$	−4.16571			−0.167299
$621$	−2.29418	+	24.8140i	−0.0920621	+	0.995753i
$622$	15.0871			0.604936
$623$		−	3.34789i		−	0.134130i
$624$	6.60218	−	6.54309i	0.264299	−	0.261933i
$625$	18.5330			0.741319
$626$	25.3150			1.01179
$627$	51.5028	+	51.9679i	2.05682	+	2.07540i
$628$			17.1304i			0.683577i
$629$		−	0.548633i		−	0.0218754i
$630$	0.0179775	−	1.99958i	0.000716241	−	0.0796654i
$631$		−	30.1918i		−	1.20192i	−0.799281	−	0.600958i	$-0.794786\pi$
$631$		−	30.1918i		−	1.20192i	0.799281	−	0.600958i	$-0.205214\pi$
$632$	5.18489			0.206244
$633$	13.9073	−	13.7828i	0.552765	−	0.547818i
$634$	20.1209			0.799102
$635$	−8.20145			−0.325465
$636$	−12.0100	+	11.9025i	−0.476228	+	0.471965i
$637$	−5.36659			−0.212632
$638$	−27.8782			−1.10371
$639$	−20.4375	−	0.183746i	−0.808495	−	0.00726887i
$640$		−	0.666555i		−	0.0263479i
$641$	42.2972			1.67064			0.835320	−	0.549764i	$-0.185282\pi$
$641$	42.2972			1.67064			0.835320	+	0.549764i	$0.185282\pi$
$642$	11.4698	+	11.5734i	0.452677	+	0.456765i
$643$		−	13.3795i		−	0.527636i	−0.964573	−	0.263818i	$-0.915018\pi$
$643$		−	13.3795i		−	0.527636i	0.964573	−	0.263818i	$-0.0849818\pi$
$644$	3.64730	−	3.11403i	0.143724	−	0.122710i
$645$	−6.47641	−	6.53490i	−0.255008	−	0.257311i
$646$	0.869430			0.0342072
$647$		−	48.6540i		−	1.91279i	−0.292085	−	0.956393i	$-0.594349\pi$
$647$		−	48.6540i		−	1.91279i	0.292085	−	0.956393i	$-0.405651\pi$
$648$	0.161818	−	8.99855i	0.00635681	−	0.353496i
$649$			11.3124i			0.444051i
$650$			24.4486i			0.958952i
$651$	7.61969	+	7.68851i	0.298639	+	0.301336i
$652$	23.2565			0.910795
$653$		−	23.3483i		−	0.913689i	−0.889547	−	0.456844i	$-0.848980\pi$
$653$		−	23.3483i		−	0.913689i	0.889547	−	0.456844i	$-0.151020\pi$
$654$	−21.6807	+	21.4866i	−0.847781	+	0.840193i
$655$		−	8.05153i		−	0.314599i
$656$		−	10.3863i		−	0.405518i
$657$	0.248671	−	27.6589i	0.00970157	−	1.07908i
$658$		−	4.18892i		−	0.163301i
$659$	−14.6786			−0.571798			−0.285899	−	0.958260i	$-0.592292\pi$
$659$	−14.6786			−0.571798			−0.285899	+	0.958260i	$0.592292\pi$
$660$	−4.38681	+	4.34754i	−0.170756	+	0.169228i
$661$		−	9.43651i		−	0.367038i	−0.983016	−	0.183519i	$-0.941251\pi$
$661$		−	9.43651i		−	0.367038i	0.983016	−	0.183519i	$-0.0587489\pi$
$662$			13.2669i			0.515631i
$663$	−0.726940	+	0.720434i	−0.0282320	+	0.0279793i
$664$			9.21786i			0.357722i
$665$	5.26331			0.204102
$666$	0.134389	−	14.9477i	0.00520746	−	0.579211i
$667$	19.0070	−	16.2280i	0.735954	−	0.628351i
$668$			1.07849i			0.0417279i
$669$	24.3963	−	24.1779i	0.943215	−	0.934774i
$670$	5.93238			0.229188
$671$			19.1942i			0.740985i
$672$	−1.23024	+	1.21923i	−0.0474575	+	0.0470327i
$673$	−41.4157			−1.59646			−0.798230	−	0.602353i	$-0.794230\pi$
$673$	−41.4157			−1.59646			−0.798230	+	0.602353i	$0.794230\pi$
$674$	9.04921			0.348563
$675$	16.5115	+	16.9629i	0.635527	+	0.652903i
$676$	−15.8003			−0.607702
$677$	9.71372			0.373329			0.186664	−	0.982424i	$-0.440232\pi$
$677$	9.71372			0.373329			0.186664	+	0.982424i	$0.440232\pi$
$678$	−0.0632291	−	0.0638001i	−0.00242830	−	0.00245023i
$679$	1.57177			0.0603191
$680$			0.0733918i			0.00281445i
$681$	33.2897	−	32.9917i	1.27566	−	1.26425i
$682$		−	33.4331i		−	1.28022i
$683$			9.83250i			0.376230i	0.982147	+	0.188115i	$0.0602378\pi$
$683$			9.83250i			0.376230i	−0.982147	+	0.188115i	$0.939762\pi$
$684$	23.6879	+	0.212969i	0.905730	+	0.00814307i
$685$	−8.04216			−0.307275
$686$	1.00000			0.0381802
$687$	−4.80993	−	4.85336i	−0.183510	−	0.185167i
$688$			7.96918i			0.303822i
$689$	52.3905			1.99592
$690$	0.460145	−	5.51767i	0.0175174	−	0.210054i
$691$	−25.8414			−0.983053			−0.491527	−	0.870863i	$-0.663561\pi$
$691$	−25.8414			−0.983053			−0.491527	+	0.870863i	$0.663561\pi$
$692$			3.31012i			0.125832i
$693$	16.0482	+	0.144283i	0.609622	+	0.00548087i
$694$	−1.98637			−0.0754018
$695$	−3.35982			−0.127445
$696$	−6.41108	+	6.35370i	−0.243011	+	0.240836i
$697$			1.14360i			0.0433169i
$698$			19.8108i			0.749851i
$699$	−13.6128	−	13.7357i	−0.514883	−	0.519533i
$700$		−	4.55570i		−	0.172189i
$701$	−10.2274			−0.386282			−0.193141	−	0.981171i	$-0.561868\pi$
$701$	−10.2274			−0.386282			−0.193141	+	0.981171i	$0.561868\pi$
$702$	−19.9822	+	19.4504i	−0.754180	+	0.734108i
$703$	39.3453			1.48394
$704$	5.34963			0.201622
$705$	−3.40426	−	3.43500i	−0.128212	−	0.129370i
$706$	26.9844			1.01557
$707$	5.49382			0.206616
$708$	2.57820	+	2.60148i	0.0968946	+	0.0977697i
$709$		−	21.9812i		−	0.825522i	−0.910839	−	0.412761i	$-0.864565\pi$
$709$		−	21.9812i		−	0.825522i	0.910839	−	0.412761i	$-0.135435\pi$
$710$	4.54109			0.170424
$711$	−15.5540	−	0.139840i	−0.583322	−	0.00524442i
$712$			3.34789i			0.125467i
$713$	19.4615	+	22.7942i	0.728839	+	0.853649i
$714$	0.135457	−	0.134244i	0.00506934	−	0.00502397i
$715$	19.1363			0.715656
$716$			16.5448i			0.618307i
$717$	−13.6684	−	13.7919i	−0.510457	−	0.515067i
$718$		−	14.2075i		−	0.530221i
$719$		−	40.0375i		−	1.49315i	−0.665302	−	0.746574i	$-0.731697\pi$
$719$		−	40.0375i		−	1.49315i	0.665302	−	0.746574i	$-0.268303\pi$
$720$	−0.0179775	+	1.99958i	−0.000669982	+	0.0745201i
$721$	13.1797			0.490838
$722$			43.3514i			1.61337i
$723$	−0.797436	−	0.804638i	−0.0296570	−	0.0299248i
$724$			7.95913i			0.295799i
$725$		−	23.7409i		−	0.881715i
$726$	−21.4809	−	21.6749i	−0.797232	−	0.804432i
$727$		−	42.1888i		−	1.56469i	−0.622842	−	0.782347i	$-0.714022\pi$
$727$		−	42.1888i		−	1.56469i	0.622842	−	0.782347i	$-0.285978\pi$
$728$	5.36659			0.198899
$729$	−0.728132	+	26.9902i	−0.0269678	+	0.999636i
$730$			6.14565i			0.227461i
$731$		−	0.877456i		−	0.0324539i
$732$	4.37454	+	4.41404i	0.161688	+	0.163148i
$733$			20.5140i			0.757702i	0.925458	+	0.378851i	$0.123681\pi$
$733$			20.5140i			0.757702i	−0.925458	+	0.378851i	$0.876319\pi$
$734$	12.5018			0.461450
$735$	0.820021	−	0.812682i	0.0302469	−	0.0299762i
$736$	−3.64730	+	3.11403i	−0.134441	+	0.114785i
$737$			47.6120i			1.75381i
$738$	−0.280127	+	31.1577i	−0.0103116	+	1.14693i
$739$	5.28881			0.194552			0.0972760	−	0.995257i	$-0.468987\pi$
$739$	5.28881			0.194552			0.0972760	+	0.995257i	$0.468987\pi$
$740$			3.32129i			0.122093i
$741$	−51.6661	−	52.1327i	−1.89800	−	1.91514i
$742$	−9.76235			−0.358387
$743$	21.6095			0.792775			0.396387	−	0.918083i	$-0.370264\pi$
$743$	21.6095			0.792775			0.396387	+	0.918083i	$0.370264\pi$
$744$	−7.61969	−	7.68851i	−0.279351	−	0.281874i
$745$	−14.3451			−0.525565
$746$	−30.0466			−1.10008
$747$	0.248613	−	27.6525i	0.00909626	−	1.01175i
$748$	−0.589026			−0.0215369
$749$			9.40743i			0.343740i
$750$	−7.76575	−	7.83588i	−0.283565	−	0.286126i
$751$		−	9.06506i		−	0.330789i	−0.986228	−	0.165394i	$-0.947110\pi$
$751$		−	9.06506i		−	0.330789i	0.986228	−	0.165394i	$-0.0528897\pi$
$752$			4.18892i			0.152754i
$753$	−18.1365	+	17.9741i	−0.660930	+	0.655014i
$754$	27.9666			1.01848
$755$	−2.64470			−0.0962503
$756$	3.72345	−	3.62435i	0.135420	−	0.131816i
$757$			7.70844i			0.280168i	0.990140	+	0.140084i	$0.0447373\pi$
$757$			7.70844i			0.280168i	−0.990140	+	0.140084i	$0.955263\pi$
$758$	6.01528			0.218485
$759$	44.2836	+	3.69302i	1.60739	+	0.134048i
$760$	−5.26331			−0.190920
$761$		−	19.5789i		−	0.709735i	−0.934917	−	0.354868i	$-0.884526\pi$
$761$		−	19.5789i		−	0.709735i	0.934917	−	0.354868i	$-0.115474\pi$
$762$	−15.0017	−	15.1371i	−0.543453	−	0.548361i
$763$	−17.6231			−0.638001
$764$	12.4324			0.449787
$765$	0.00197943	−	0.220166i	7.15665e−5	−	0.00796013i
$766$			9.66651i			0.349265i
$767$		−	11.3483i		−	0.409762i
$768$	1.23024	−	1.21923i	0.0443924	−	0.0439951i
$769$		−	20.5340i		−	0.740475i	−0.928937	−	0.370238i	$-0.879276\pi$
$769$		−	20.5340i		−	0.740475i	0.928937	−	0.370238i	$-0.120724\pi$
$770$	−3.56582			−0.128503
$771$	0.00935288	+	0.00943735i	0.000336836	+	0.000339878i
$772$	18.3412			0.660115
$773$	10.4539			0.375999			0.188000	−	0.982169i	$-0.439800\pi$
$773$	10.4539			0.375999			0.188000	+	0.982169i	$0.439800\pi$
$774$	0.214935	−	23.9066i	0.00772568	−	0.859304i
$775$	28.4714			1.02272
$776$	−1.57177			−0.0564233
$777$	6.12998	−	6.07512i	0.219912	−	0.217944i
$778$			15.2370i			0.546271i
$779$	−82.0135			−2.93844
$780$	4.40072	−	4.36133i	0.157571	−	0.156161i
$781$			36.4458i			1.30413i
$782$	0.401590	−	0.342874i	0.0143608	−	0.0122612i
$783$	19.4038	−	18.8874i	0.693436	−	0.674981i
$784$	−1.00000			−0.0357143
$785$			11.4183i			0.407538i
$786$	14.8604	−	14.7274i	0.530054	−	0.525310i
$787$		−	3.23493i		−	0.115313i	−0.998336	−	0.0576564i	$-0.981637\pi$
$787$		−	3.23493i		−	0.115313i	0.998336	−	0.0576564i	$-0.0183628\pi$
$788$		−	3.51591i		−	0.125249i
$789$	22.5000	−	22.2986i	0.801020	−	0.793850i
$790$	3.45601			0.122959
$791$		−	0.0518600i		−	0.00184393i
$792$	−16.0482	−	0.144283i	−0.570249	−	0.00512689i
$793$		−	19.2551i		−	0.683768i
$794$			9.78621i			0.347299i
$795$	−8.00533	+	7.93368i	−0.283920	+	0.281379i
$796$			5.43544i			0.192654i
$797$	−19.6728			−0.696846			−0.348423	−	0.937337i	$-0.613283\pi$
$797$	−19.6728			−0.696846			−0.348423	+	0.937337i	$0.613283\pi$
$798$	9.62737	+	9.71432i	0.340805	+	0.343883i
$799$		−	0.461225i		−	0.0163170i
$800$			4.55570i			0.161068i
$801$	0.0902951	−	10.0433i	0.00319042	−	0.354861i
$802$		−	32.1639i		−	1.13575i
$803$	−49.3236			−1.74059
$804$	10.8512	+	10.9492i	0.382692	+	0.386148i
$805$	2.43113	−	2.07567i	0.0856859	−	0.0731579i
$806$			33.5391i			1.18136i
$807$	4.40545	+	4.44524i	0.155079	+	0.156480i
$808$	−5.49382			−0.193272
$809$			50.2084i			1.76524i	0.470092	+	0.882618i	$0.344221\pi$
$809$			50.2084i			1.76524i	−0.470092	+	0.882618i	$0.655779\pi$
$810$	0.107861	−	5.99803i	0.00378984	−	0.210749i
$811$	−4.26994			−0.149938			−0.0749689	−	0.997186i	$-0.523886\pi$
$811$	−4.26994			−0.149938			−0.0749689	+	0.997186i	$0.523886\pi$
$812$	−5.21125			−0.182879
$813$	14.9647	−	14.8308i	0.524836	−	0.520139i
$814$	−26.6559			−0.934289
$815$	15.5017			0.543002
$816$	−0.135457	+	0.134244i	−0.00474193	+	0.00469949i
$817$	62.9270			2.20154
$818$			1.12230i			0.0392404i
$819$	−16.0991	−	0.144741i	−0.562548	−	0.00505766i
$820$		−	6.92306i		−	0.241764i
$821$			1.59879i			0.0557982i	0.999611	+	0.0278991i	$0.00888171\pi$
$821$			1.59879i			0.0557982i	−0.999611	+	0.0278991i	$0.991118\pi$
$822$	−14.7103	−	14.8431i	−0.513081	−	0.517714i
$823$	27.1689			0.947049			0.473524	−	0.880781i	$-0.342982\pi$
$823$	27.1689			0.947049			0.473524	+	0.880781i	$0.342982\pi$
$824$	−13.1797			−0.459137
$825$	29.9825	−	29.7142i	1.04386	−	1.03451i
$826$			2.11462i			0.0735769i
$827$	2.42695			0.0843932			0.0421966	−	0.999109i	$-0.486564\pi$
$827$	2.42695			0.0843932			0.0421966	+	0.999109i	$0.486564\pi$
$828$	11.0254	−	9.24335i	0.383161	−	0.321229i
$829$	−0.482502			−0.0167580			−0.00837899	−	0.999965i	$-0.502667\pi$
$829$	−0.482502			−0.0167580			−0.00837899	+	0.999965i	$0.502667\pi$
$830$			6.14421i			0.213269i
$831$	20.7624	−	20.5765i	0.720239	−	0.713792i
$832$	−5.36659			−0.186053
$833$	0.110106			0.00381495
$834$	−6.14560	−	6.20110i	−0.212805	−	0.214727i
$835$			0.718871i			0.0248776i
$836$		−	42.2422i		−	1.46098i
$837$	22.6508	+	23.2701i	0.782926	+	0.804332i
$838$			15.3482i			0.530193i
$839$	−11.8225			−0.408159			−0.204080	−	0.978954i	$-0.565420\pi$
$839$	−11.8225			−0.408159			−0.204080	+	0.978954i	$0.565420\pi$
$840$	−0.820021	+	0.812682i	−0.0282934	+	0.0280402i
$841$	1.84288			0.0635476
$842$	23.1332			0.797222
$843$	33.3982	−	33.0993i	1.15029	−	1.14000i
$844$	−11.3045			−0.389119
$845$	−10.5317			−0.362303
$846$	0.112978	−	12.5662i	0.00388427	−	0.432036i
$847$		−	17.6185i		−	0.605378i
$848$	9.76235			0.335240
$849$	−10.8070	−	10.9046i	−0.370895	−	0.374245i
$850$		−	0.501611i		−	0.0172051i
$851$	18.1736	−	15.5165i	0.622984	−	0.531898i
$852$	8.30632	+	8.38133i	0.284570	+	0.287140i
$853$	−47.7621			−1.63534			−0.817672	−	0.575684i	$-0.804736\pi$
$853$	−47.7621			−1.63534			−0.817672	+	0.575684i	$0.804736\pi$
$854$			3.58796i			0.122777i
$855$	15.7893	+	0.141956i	0.539983	+	0.00485478i
$856$		−	9.40743i		−	0.321539i
$857$			17.7383i			0.605929i	0.953002	+	0.302964i	$0.0979763\pi$
$857$			17.7383i			0.605929i	−0.953002	+	0.302964i	$0.902024\pi$
$858$	35.0031	+	35.3192i	1.19498	+	1.20578i
$859$	−36.3523			−1.24032			−0.620162	−	0.784474i	$-0.712933\pi$
$859$	−36.3523			−1.24032			−0.620162	+	0.784474i	$0.712933\pi$
$860$			5.31190i			0.181134i
$861$	−12.7777	+	12.6633i	−0.435461	+	0.431564i
$862$			20.8892i			0.711488i
$863$			0.721182i			0.0245493i	0.999925	+	0.0122747i	$0.00390724\pi$
$863$			0.721182i			0.0245493i	−0.999925	+	0.0122747i	$0.996093\pi$
$864$	−3.72345	+	3.62435i	−0.126674	+	0.123303i
$865$			2.20638i			0.0750192i
$866$	23.7880			0.808350
$867$	−20.8991	+	20.7121i	−0.709772	+	0.703419i
$868$		−	6.24961i		−	0.212126i
$869$			27.7372i			0.940920i
$870$	−4.27334	+	4.23509i	−0.144880	+	0.143583i
$871$		−	47.7630i		−	1.61839i
$872$	17.6231			0.596795
$873$	4.71513	+	0.0423919i	0.159583	+	0.00143475i
$874$	24.5893	+	28.8001i	0.831746	+	0.974179i
$875$		−	6.36940i		−	0.215325i
$876$	−11.3428	+	11.2413i	−0.383238	+	0.379808i
$877$	7.53311			0.254375			0.127188	−	0.991879i	$-0.459405\pi$
$877$	7.53311			0.254375			0.127188	+	0.991879i	$0.459405\pi$
$878$		−	1.21747i		−	0.0410875i
$879$	−34.1337	+	33.8282i	−1.15130	+	1.14100i
$880$	3.56582			0.120204
$881$	16.3348			0.550332			0.275166	−	0.961397i	$-0.411267\pi$
$881$	16.3348			0.550332			0.275166	+	0.961397i	$0.411267\pi$
$882$	2.99988	+	0.0269708i	0.101011	+	0.000908153i
$883$	48.2010			1.62209			0.811047	−	0.584981i	$-0.198898\pi$
$883$	48.2010			1.62209			0.811047	+	0.584981i	$0.198898\pi$
$884$	0.590894			0.0198739
$885$	1.71851	+	1.73403i	0.0577671	+	0.0582888i
$886$	−16.8190			−0.565046
$887$			47.1980i			1.58475i	0.610031	+	0.792377i	$0.291157\pi$
$887$			47.1980i			1.58475i	−0.610031	+	0.792377i	$0.708843\pi$
$888$	−6.12998	+	6.07512i	−0.205709	+	0.203868i
$889$		−	12.3042i		−	0.412671i
$890$			2.23155i			0.0748018i
$891$	48.1388	+	0.865666i	1.61271	+	0.0290009i
$892$	−19.8306			−0.663976
$893$	33.0769			1.10688
$894$	−26.2394	−	26.4763i	−0.877576	−	0.885501i
$895$			11.0280i			0.368625i
$896$	1.00000			0.0334077
$897$	−44.4240	−	3.70473i	−1.48327	−	0.123697i
$898$	−15.8862			−0.530129
$899$		−	32.5683i		−	1.08621i
$900$	0.122871	−	13.6666i	0.00409569	−	0.455552i
$901$	−1.07489			−0.0358099
$902$	55.5630			1.85004
$903$	9.80399	−	9.71624i	0.326256	−	0.323336i
$904$			0.0518600i			0.00172484i
$905$			5.30520i			0.176351i
$906$	−4.83754	−	4.88122i	−0.160716	−	0.162168i
$907$		−	16.4274i		−	0.545464i	−0.962090	−	0.272732i	$-0.912073\pi$
$907$		−	16.4274i		−	0.545464i	0.962090	−	0.272732i	$-0.0879272\pi$
$908$	−27.0595			−0.898002
$909$	16.4808	+	0.148173i	0.546634	+	0.00491457i
$910$	3.57713			0.118581
$911$	19.9533			0.661082			0.330541	−	0.943792i	$-0.392769\pi$
$911$	19.9533			0.661082			0.330541	+	0.943792i	$0.392769\pi$
$912$	−9.62737	−	9.71432i	−0.318794	−	0.321673i
$913$	−49.3121			−1.63199
$914$	40.2479			1.33128
$915$	2.91587	+	2.94220i	0.0963957	+	0.0972662i
$916$			3.94506i			0.130349i
$917$	12.0793			0.398894
$918$	0.409974	−	0.399063i	0.0135312	−	0.0131711i
$919$			43.5181i			1.43553i	0.696286	+	0.717765i	$0.254835\pi$
$919$			43.5181i			1.43553i	−0.696286	+	0.717765i	$0.745165\pi$
$920$	−2.43113	+	2.07567i	−0.0801519	+	0.0684330i
$921$	40.8181	−	40.4528i	1.34500	−	1.33297i
$922$	−12.1963			−0.401664
$923$		−	36.5613i		−	1.20343i
$924$	−6.52241	−	6.58131i	−0.214571	−	0.216509i
$925$		−	22.7000i		−	0.746371i
$926$		−	19.8584i		−	0.652587i
$927$	39.5376	+	0.355467i	1.29858	+	0.0116751i
$928$	5.21125			0.171068
$929$		−	6.38397i		−	0.209451i	−0.994501	−	0.104726i	$-0.966604\pi$
$929$		−	6.38397i		−	0.209451i	0.994501	−	0.104726i	$-0.0333964\pi$
$930$	−5.07894	−	5.12481i	−0.166545	−	0.168049i
$931$			7.89629i			0.258790i
$932$			11.1651i			0.365725i
$933$	18.3946	+	18.5607i	0.602211	+	0.607650i
$934$			9.92975i			0.324912i
$935$	−0.392618			−0.0128400
$936$	16.0991	+	0.144741i	0.526216	+	0.00473100i
$937$		−	24.5988i		−	0.803609i	−0.915726	−	0.401804i	$-0.868383\pi$
$937$		−	24.5988i		−	0.803609i	0.915726	−	0.401804i	$-0.131617\pi$
$938$			8.90006i			0.290597i
$939$	30.8648	+	31.1435i	1.00723	+	1.01633i
$940$			2.79214i			0.0910697i
$941$	−58.8031			−1.91693			−0.958464	−	0.285214i	$-0.907935\pi$
$941$	−58.8031			−1.91693			−0.958464	+	0.285214i	$0.907935\pi$
$942$	−21.0744	+	20.8858i	−0.686642	+	0.680497i
$943$	−37.8821	+	32.3434i	−1.23361	+	1.05325i
$944$		−	2.11462i		−	0.0688249i
$945$	2.48188	−	2.41583i	0.0807357	−	0.0785870i
$946$	−42.6321			−1.38609
$947$		−	26.9622i		−	0.876154i	−0.898938	−	0.438077i	$-0.855660\pi$
$947$		−	26.9622i		−	0.876154i	0.898938	−	0.438077i	$-0.144340\pi$
$948$	6.32156	+	6.37865i	0.205315	+	0.207169i
$949$	49.4800			1.60619
$950$	35.9732			1.16712
$951$	24.5319	+	24.7535i	0.795502	+	0.802686i
$952$	−0.110106			−0.00356856
$953$	1.01959			0.0330277			0.0165139	−	0.999864i	$-0.494743\pi$
$953$	1.01959			0.0330277			0.0165139	+	0.999864i	$0.494743\pi$
$954$	−29.2859	−	0.263298i	−0.948165	−	0.00852458i
$955$	8.28686			0.268156
$956$			11.2107i			0.362581i
$957$	−33.9899	−	34.2969i	−1.09874	−	1.10866i
$958$		−	13.8661i		−	0.447993i
$959$		−	12.0653i		−	0.389608i
$960$	0.820021	−	0.812682i	0.0264661	−	0.0262292i
$961$	8.05761			0.259923
$962$	26.7404			0.862146
$963$	−0.253726	+	28.2212i	−0.00817619	+	0.909414i
$964$			0.654051i			0.0210656i
$965$	12.2254			0.393550
$966$	8.27789	+	0.690333i	0.266337	+	0.0222111i
$967$	8.81613			0.283508			0.141754	−	0.989902i	$-0.454726\pi$
$967$	8.81613			0.283508			0.141754	+	0.989902i	$0.454726\pi$
$968$			17.6185i			0.566280i
$969$	1.06003	+	1.06961i	0.0340531	+	0.0343607i
$970$	−1.04767			−0.0336387
$971$	−0.963131			−0.0309084			−0.0154542	−	0.999881i	$-0.504919\pi$
$971$	−0.963131			−0.0309084			−0.0154542	+	0.999881i	$0.504919\pi$
$972$	11.2676	−	10.7722i	0.361410	−	0.345518i
$973$		−	5.04057i		−	0.161593i
$974$			11.2926i			0.361837i
$975$	−30.0776	+	29.8084i	−0.963253	+	0.954632i
$976$		−	3.58796i		−	0.114848i
$977$	−47.2621			−1.51205			−0.756025	−	0.654543i	$-0.772861\pi$
$977$	−47.2621			−1.51205			−0.756025	+	0.654543i	$0.772861\pi$
$978$	28.3550	+	28.6110i	0.906692	+	0.914880i
$979$	−17.9099			−0.572404
$980$	−0.666555			−0.0212923
$981$	−52.8673	−	0.475309i	−1.68792	−	0.0151755i
$982$	12.9002			0.411661
$983$	−6.71485			−0.214170			−0.107085	−	0.994250i	$-0.534152\pi$
$983$	−6.71485			−0.214170			−0.107085	+	0.994250i	$0.534152\pi$
$984$	12.7777	−	12.6633i	0.407337	−	0.403691i
$985$		−	2.34354i		−	0.0746715i
$986$	−0.573790			−0.0182732
$987$	5.15336	−	5.10724i	0.164033	−	0.162565i
$988$			42.3761i			1.34816i
$989$	29.0660	−	24.8163i	0.924245	−	0.789113i
$990$	−10.6970	−	0.0961729i	−0.339974	−	0.00305657i
$991$	−2.46742			−0.0783801			−0.0391900	−	0.999232i	$-0.512478\pi$
$991$	−2.46742			−0.0783801			−0.0391900	+	0.999232i	$0.512478\pi$
$992$			6.24961i			0.198425i
$993$	−16.3214	+	16.1753i	−0.517943	+	0.513308i
$994$			6.81278i			0.216088i
$995$			3.62302i			0.114858i
$996$	−11.3402	+	11.2387i	−0.359327	+	0.356111i
$997$	24.4111			0.773106			0.386553	−	0.922267i	$-0.373666\pi$
$997$	24.4111			0.773106			0.386553	+	0.922267i	$0.373666\pi$
$998$			0.583048i			0.0184561i
$999$	18.5531	−	18.0593i	0.586993	−	0.571371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.b.827.9	yes	24
3.2	odd	2		966.2.h.a.827.21	yes	24
23.22	odd	2		966.2.h.a.827.9	✓	24
69.68	even	2	inner	966.2.h.b.827.21	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.9	✓	24	23.22	odd	2
966.2.h.a.827.21	yes	24	3.2	odd	2
966.2.h.b.827.9	yes	24	1.1	even	1	trivial
966.2.h.b.827.21	yes	24	69.68	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.23024 - 1.21923i) q^{3} -1.00000 q^{4} -0.666555 q^{5} +(-1.21923 - 1.23024i) q^{6} -1.00000i q^{7} +1.00000i q^{8} +(0.0269708 - 2.99988i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.23024 - 1.21923i) q^{3} -1.00000 q^{4} -0.666555 q^{5} +(-1.21923 - 1.23024i) q^{6} -1.00000i q^{7} +1.00000i q^{8} +(0.0269708 - 2.99988i) q^{9} +0.666555i q^{10} -5.34963 q^{11} +(-1.23024 + 1.21923i) q^{12} +5.36659 q^{13} -1.00000 q^{14} +(-0.820021 + 0.812682i) q^{15} +1.00000 q^{16} -0.110106 q^{17} +(-2.99988 - 0.0269708i) q^{18} -7.89629i q^{19} +0.666555 q^{20} +(-1.21923 - 1.23024i) q^{21} +5.34963i q^{22} +(-3.11403 - 3.64730i) q^{23} +(1.21923 + 1.23024i) q^{24} -4.55570 q^{25} -5.36659i q^{26} +(-3.62435 - 3.72345i) q^{27} +1.00000i q^{28} +5.21125i q^{29} +(0.812682 + 0.820021i) q^{30} -6.24961 q^{31} -1.00000i q^{32} +(-6.58131 + 6.52241i) q^{33} +0.110106i q^{34} +0.666555i q^{35} +(-0.0269708 + 2.99988i) q^{36} +4.98276i q^{37} -7.89629 q^{38} +(6.60218 - 6.54309i) q^{39} -0.666555i q^{40} -10.3863i q^{41} +(-1.23024 + 1.21923i) q^{42} +7.96918i q^{43} +5.34963 q^{44} +(-0.0179775 + 1.99958i) q^{45} +(-3.64730 + 3.11403i) q^{46} +4.18892i q^{47} +(1.23024 - 1.21923i) q^{48} -1.00000 q^{49} +4.55570i q^{50} +(-0.135457 + 0.134244i) q^{51} -5.36659 q^{52} +9.76235 q^{53} +(-3.72345 + 3.62435i) q^{54} +3.56582 q^{55} +1.00000 q^{56} +(-9.62737 - 9.71432i) q^{57} +5.21125 q^{58} -2.11462i q^{59} +(0.820021 - 0.812682i) q^{60} -3.58796i q^{61} +6.24961i q^{62} +(-2.99988 - 0.0269708i) q^{63} -1.00000 q^{64} -3.57713 q^{65} +(6.52241 + 6.58131i) q^{66} -8.90006i q^{67} +0.110106 q^{68} +(-8.27789 - 0.690333i) q^{69} +0.666555 q^{70} -6.81278i q^{71} +(2.99988 + 0.0269708i) q^{72} +9.22001 q^{73} +4.98276 q^{74} +(-5.60460 + 5.55444i) q^{75} +7.89629i q^{76} +5.34963i q^{77} +(-6.54309 - 6.60218i) q^{78} -5.18489i q^{79} -0.666555 q^{80} +(-8.99855 - 0.161818i) q^{81} -10.3863 q^{82} +9.21786 q^{83} +(1.21923 + 1.23024i) q^{84} +0.0733918 q^{85} +7.96918 q^{86} +(6.35370 + 6.41108i) q^{87} -5.34963i q^{88} +3.34789 q^{89} +(1.99958 + 0.0179775i) q^{90} -5.36659i q^{91} +(3.11403 + 3.64730i) q^{92} +(-7.68851 + 7.61969i) q^{93} +4.18892 q^{94} +5.26331i q^{95} +(-1.21923 - 1.23024i) q^{96} +1.57177i q^{97} +1.00000i q^{98} +(-0.144283 + 16.0482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9	\( 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 24 q^{14} + 4 q^{15} + 24 q^{16} - 32 q^{17} + 4 q^{18} - 4 q^{20} + 8 q^{23} - 12 q^{25} + 16 q^{27} + 4 q^{30} - 16 q^{31} - 20 q^{33} + 4 q^{36} - 8 q^{39} - 4 q^{42} - 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} - 24 q^{51} - 8 q^{52} - 24 q^{53} - 12 q^{54} + 16 q^{55} + 24 q^{56} - 4 q^{57} + 4 q^{58} - 4 q^{60} + 4 q^{63} - 24 q^{64} + 12 q^{66} + 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} + 16 q^{74} + 48 q^{75} + 12 q^{78} + 4 q^{80} - 8 q^{81} - 8 q^{82} - 16 q^{83} - 16 q^{85} - 16 q^{86} + 20 q^{87} - 24 q^{89} + 28 q^{90} - 8 q^{92} + 16 q^{93} + 8 q^{94} + 48 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 24 * q^14 + 4 * q^15 + 24 * q^16 - 32 * q^17 + 4 * q^18 - 4 * q^20 + 8 * q^23 - 12 * q^25 + 16 * q^27 + 4 * q^30 - 16 * q^31 - 20 * q^33 + 4 * q^36 - 8 * q^39 - 4 * q^42 - 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 - 24 * q^51 - 8 * q^52 - 24 * q^53 - 12 * q^54 + 16 * q^55 + 24 * q^56 - 4 * q^57 + 4 * q^58 - 4 * q^60 + 4 * q^63 - 24 * q^64 + 12 * q^66 + 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 + 16 * q^74 + 48 * q^75 + 12 * q^78 + 4 * q^80 - 8 * q^81 - 8 * q^82 - 16 * q^83 - 16 * q^85 - 16 * q^86 + 20 * q^87 - 24 * q^89 + 28 * q^90 - 8 * q^92 + 16 * q^93 + 8 * q^94 + 48 * q^99

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